The dynamic impact of fear effects and role reversal on standard incidence ecological models

In ecosystems, the relationship between predators and prey is complex and dynamic. This paper constructs an eco-epidemiological model, incorporating a standard incidence rate and anti-predator behavior, and considers the infection of predator populations by parasites as well as the potential role reversal between infected predators and prey. Through mathematical analysis, we demonstrate the existence and local stability of the system's equilibria and verify the occurrence of Hopf bifurcation. Theoretical and numerical simulation results show that the fear effect can reduce the density of the predator population but has a relatively minor impact on the density of the prey population. Moreover, the cost of the fear effect may not only destabilize the system's equilibrium but also induce a transition from an unstable to a stable state. Based on the above theoretical analysis, we confirm that introducing parasites into the predator population is an effective method to protect endangered prey.